Download Efficient seeding techniques for protein similarity search

Efficient seeding techniques for
protein similarity search
Mikhail Roytberg1 , Anna Gambin2 , Laurent Noé3 , Slawomir Lasota2 ,
Eugenia Furletova1 , Ewa Szczurek4 , and Gregory Kucherov3
1
Institute of Mathematical Problems in Biology, Pushchino, Moscow Region,
142290, Russia, [email protected],[email protected]
2
Institute of Informatics, Warsaw University, Banacha 2, 02-097, Poland,
{aniag|S.Lasota}@mimuw.edu.pl
3
LIFL/CNRS/INRIA, Bât. M3, Campus Scientifique, 59655 Villeneuve d’Ascq
Cédex, France, {Gregory.Kucherov|Laurent.Noe}@lifl.fr
4
Max Planck Institute for Molecular Genetics, Computational Molecular Biology,
Ihnestr. 73, 14195 Berlin, Germany, [email protected]
Abstract. We apply the concept of subset seeds proposed in [1] to similarity search in protein sequences. The main question studied is the
design of efficient seed alphabets to construct seeds with optimal sensitivity/selectivity trade-offs. We propose several different design methods
and use them to construct several alphabets. We then perform an analysis
of seeds built over those alphabet and compare them with the standard
Blastp seeding method [2,3], as well as with the family of vector seeds
proposed in [4]. While the formalism of subset seed is less expressive
(but less costly to implement) than the accumulative principle used in
Blastp and vector seeds, our seeds show a similar or even better performance than Blastp on Bernoulli models of proteins compatible with
the common BLOSUM62 matrix.
1
Introduction
Similarity search in protein sequences is probably the most classical bioinformatics problem, and a commonly used algorithmic solution is implemented in
the ubiquitous Blast software [2,3]. On the other hand, similarity search algorithms for nucleotide sequences (DNA, RNA) underwent several years ago a
significant improvement due to the idea of spaced seeds and its various generalizations [5,6,7,8,9,10,11]. This development, however, has little affected protein
sequence comparison, although improving the speed/precision trade-off for protein search would be of great value for numerous bioinformatics projects. Due
to a bigger alphabet size, protein seeds are much shorter (typically 2-5 letters
instead of 10-20 letters in the DNA case) and also letter identity is much less relevant in defining hits than in the DNA case. For these reasons, the spaced seeds
technique might seem not to apply directly to protein sequence comparison.
Recall that Blast applies quite different approaches to protein and DNA
sequences to define a hit. In the DNA case, a hit is defined as a short pattern
2
M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
of identically matching nucleotides whereas in the protein case, a hit is defined
through an accumulative contribution of a few amino acid matches (not necessarily identities) using a given scoring matrix. Defining a hit through an additive
contribution of several positions is captured by a general formalism of vector
seeds proposed in [7]. On the other hand, it has been understood [6,12,13,14,15]
that using simultaneously a family of seeds instead of a single seed can further
improve the sensitivity/selectivity ratio. Papers [4,16] both propose solutions
using a family of vector seeds to surpass the performance of Blast.
However, using the principle of accumulative score over several adjacent positions has an algorithmic cost. Defining a hit through a pattern of exact letter
matches allows for a direct hashing scheme, where each key of the query sequence
is associated with a unique hash table entry storing positions of the subject sequence (database) where the key can hit. On the other hand, defining a hit
through an accumulative contribution of several positions leads to an additional
pre-computed table storing, for each key, its neighborhood i.e., the list of subject
keys (or corresponding hash table entries) with which it can form a hit. For example, in a standard Blastp setting (Blosum62 scoring matrix with threshold
11 for accumulative score of 3 contiguous positions) a 3-letter key hits on average
19.34 distinct keys, i.e. requires that many accesses to the hash table. For the
family of vector seeds from [4] with an equivalent selectivity level (score 18), a
(here 4-letter) key hits on average 15.99 keys. For some applications, for example
in setting large-scale protein comparisons on a specialized computer architecture
(see e.g. [17]) one might need to minimize the number of hash table accesses,
and therefore to use another seeding formalism.
In [1], we proposed a new concept of subset seeds that can be viewed as an
intermediate between ordinary spaced seeds and vector seeds: subset seeds allow one to distinguish between different types of mismatches (or matches) but
still treat seed positions independently rather than cumulatively. Distinguishing different mismatches is not done by scoring them, but by extending the
seed alphabet such that each seed letter specifies different sets of mismatches.
For example, in the DNA case it is beneficial to distinguish between transition
mutations (A ↔ G, C ↔ T) and others (transversions) [18].
Since the protein alphabet is much larger than the one of DNA, subset seeds
provide a very attractive seeding option for protein alignment. The present study
is then motivated by following general questions: how far can we go with subset
seeds applied to protein sequences? Can we reach the performance of Blast
seeds? the one of vector seeds? or maybe even outperform them? . . .
In the paradigm of subset seeds, each seed letter specifies a set of amino acid
pairs matched by this letter. Therefore, a crucial question is the design of an
appropriate seed alphabet, which is one of the main problems we study in this
paper. In Section 2, we introduce some probabilistic notions we need to reason
about seed efficiency. Section 3 introduces the first simple approach to design a
seed alphabet, which, however, does not lead to so-called transitive seeds, useful
in practice. Section 4 presents three different approaches to designing transitive
seed alphabets, based on a pre-defined (Section 4.1) or newly designed (Sec-
subset seeds for protein similarity search
3
tion 4.2) hierarchical clustering of amino acids, as well as on a non-hierarchical
clustering (Section 4.3). Section 5 describes comparative experiments made with
the designed seeds on probabilistic models.
2
Preliminaries
Throughout the paper, Σ = {A, C, D, E, F, G, H, I, K, L, M, N, P, Q, R, S, T, V, W, Y} denotes the alphabet of amino acids.
In most general terms, a (subset) seed letter α is defined as any symmetric
and reflexive binary relation on Σ. Let B be a seed alphabet, i.e. a collection
of subset seed letters. Then a subset seed π = α1 . . . αk is a word over B. π
defines a symmetric and reflexive binary relation on words of Σ k (called keys):
for s1 , s2 ∈ Σ k , s1 ∼π s2 iff ∀i ∈ [1..k], we have hs1 [i], s2 [i]i ∈ αi .
For practical reasons, we would like seed letters to define a transitive relation, in addition. This induces an equivalence relation on keys, which is very
convenient and allows for an efficient indexing scheme (see Introduction). In
this paper, we will be mainly interested in transitive seed letters, but we will
also study the non-transitive case in order to see how restrictive the transitivity
condition is.
The quality of a seed letter or of a seed is characterized by two main parameters: sensitivity and selectivity. They are defined through background and
foreground probabilistic models of protein alignments. Foreground probabilities
are assumed to represent the distribution of amino acids matches in proteins of
interest, when two homologous proteins are aligned together. Background probabilities, on the other hand, represent the distribution of amino acid matches in
random alignments, when two proteins are randomly aligned together.
In this paper, we restrict ourselves to Bernoulli models of proteins and protein
alignments, although some of the results we will present can be extended to
Markov models.
Assume that we are given background probabilities {b1 , . . . , b20 } of amino
acids in protein sequences under
P interest. The background probability of a seed
letter α is defined by b(α) = (ai ,aj )∈α bi bj . The selectivity of α is 1 − b(α) and
the weight of α is defined by
w(α) =
log b(α)
,
log b(#)
(1)
where # = {ha, ai|a ∈ Σ} is the “identity” seed letter. For a seed π = α1 . . . αk ,
Qk
the background probability of π is b(π) = i=1 b(αi ), the selectivity of π is
Pk
1 − b(π) and the weight of π is w(π) = logb(#) b(π) = i=1 w(αi ). Note that the
weight here generalizes the weight of of classical spaced seeds [19] defined as the
number of “identity” letters it contains.
Let fij be the probability to see a pair hai , aj i aligned in a target
P alignment.
The foreground probability of a seed letter α is defined by f (α) = (ai ,aj )∈α fij .
The sensitivity of a seed π is defined as the probability to hit a random target
4
M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
alignment5 . Assume that target alignments are specified by a length N . Then
the sensitivity of a seed π = α1 . . . αk is the probability that a randomly drawn
gapless alignment (i.e. string of pairs hai , aj i) of length N contains a fragment
of length k which is matched by π. In [1] we proposed a general algorithm to
efficiently compute the seed sensitivity for a broad class of target alignment
models. This algorithm will be used in the experimental part of this work.
The general problem of seed design is to obtain seeds with good sensitivity/selectivity trade-off. Even within a fixed seed formalism, the quality of a
seed is dependent on the chosen selectivity value. This is why we will always be
interested in computing efficient seeds for a large range of selectivity levels.
3
Dominating seed letters
Our main question is how to choose seed letters that form good seeds? Intuitively,
“good letters” are those that best distinguish foreground and background letter
alignments.
For each letter α, consider its foreground and background probabilities f (α)
and b(α) respectively. Intuitively, we would like to have letters α with large f (α)
and small b(α). A letter α is said to dominate a letter β if f (α) ≥ f (β) and
b(α) ≤ b(β). Observe that in this case, β can be removed from consideration, as
it can be always advantageously replaced by α.
Consider all amino acid pairs (ai , aj ) ordered by descending likelihood ratio fij /bi bj . Consider the set of pairs (ai , aj ) such that fij /bi bj > s for some
threshold value s. Then one can show that this set forms a letter that cannot be
dominated by any other letter6 (proof omitted). This observation leads to defining seed letters that consist of those pairs (ai , aj ) for which the ratio fij /bi bj is
above a given threshold.
Resulting alphabet We computed the likelihood ratio for all amino acid pairs,
based on practical values of background and foreground probabilities computed
in accordance with the BLOSUM62 matrix (see Section 5.1). Not surprisingly,
amino acid identities (pairs ha, ai) have highest likelihood scores varying from
38.11 for tryptophan down to 3.69 for valine. Among distinct pairs, only 25 have
a score greater than 1 (Figure 1). A quick analysis shows that those do not form
transitive relations, and therefore do not verify the transitivity requirement. The
alphabet containing those 25 pairs is denoted Non-transitive. It will be used in
the experimental part of the paper (Section 5) in order to study how restrictive
5
6
Note that our definitions of sensitivity and selectivity are not symmetric: sensitivity
is defined with respect to the entire alignment and selectivity with respect to a
single alignment position. These definitions capture better the intended parameters
we want to measure. However, selectivity could also be defined with respect to the
entire alignment. We could suggest the term specificity for this latter definition.
It is interesting to point out the relationship to the well-known Neyman-Pearson
lemma which is a more general formulation of this statement.
subset seeds for protein similarity search
5
Fig. 1. Alphabet Non-transitive: amino acid pairs with likelihood ratio > 1
is the requirement of transitive letters, i.e. how much better are general seeds
than those obtained with the restriction of transitivity.
4
Transitive seed alphabets
In the case of transitive seed alphabets, every letter α ∈ B is a partition of the
amino acid alphabet Σ. In other words, the binary relation associated with each
letter (cf Section 2) is an equivalence relation. Transitive alphabets represent the
practical case when each amino acid is uniquely mapped to its equivalence class.
This, in turn, allows for an efficient hashing scheme during the stage of seed
search, when different entries of the hash table index non-intersecting subsets of
keys.
In Sections 4.1,4.2, we explore transitive seed alphabets verifying an additional condition: for any two seed letters α1 , α2 ∈ B corresponding to partitions
Pα1 , Pα2 respectively, one of Pα1 , Pα2 is a refinement of the other. Formally, for
any α1 , α2 ∈ B,
either every set σ ∈ Pα1 is a subset of some δ ∈ Pα2 , or vice versa.
(2)
The purpose of the above requirement is to define seed letters using a biologically significant hierarchical clustering of amino acids represented by a tree.
In Section 4.1, we will use a pre-defined hierarchical clustering to design efficient seed alphabets. Then in Section 4.2, we construct our own clustering based
on appropriate background and foreground models of amino acids distribution.
Finally, in Section 4.3 we lift condition (2) and study “non-hierarchical” seed
alphabets.
4.1
Transitive alphabets based on a pre-defined clustering
Assume we have a biologically significant hierarchical clustering tree which is a
rooted binary tree T with 20 leaves labelled by amino acids. Such trees have been
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M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
proposed in [20,21], based on different similarity relations. The hierarchical tree
derived from [20] is shown on Figure 2. The tree, obtained with a purely bioinfor-
CFYWMLIVGPATSNHQEDRK
CFYWMLIV
GPATSNHQEDRK
MLIW
GPATS
CFYW
F
C
FYW
FY
W
Y
M
ML
IV
L
I
G
V
NHQEDRK
PATS
NHQED
P
ATS
A
TS
T
N
S
RK
NH
QED
R
H
QE
D
Q
K
E
Fig. 2. Hierarchical tree derived from [20].
matics analysis, groups together amino acids with similar biochemical properties,
such as hydrophobic amino acids L,M,I,V, hydrophobic aromatic amino acids
F,Y,W, alcohols S,T, or charged/polar amino acids E,D,N,Q. A similar grouping
is obtained in [21].
A seed letter is defined here as a subset α of nodes of T such that
(i) α contains all leaves,
(ii) for a node v, if v ∈ α, then all descendants of v belong to α too.
In other words, a seed letter can be thought of as a “horizontal cut” of the tree.
For example, for the tree of Figure 2 there are 1597 different seed letters. Seed
letters are naturally ordered by inclusion. The smallest one is the “identity” seed
letter #, containing only the leaves. The largest one is the “joker” seed letter ,
containing all the nodes of T . One particular seed letter is obtained by removing
from the root node. We denote it by @.
Observe that each seed letter α represents naturally an equivalence relation
on Σ: ai and aj are related iff their common ancestor belongs to α. It is identity
relation in case of # and full relation in case of .
Following condition (2), a hierarchical seed alphabet is a family B of seed
letters such that
for every α1 , α2 ∈ B, either α1 ⊆ α2 or α2 ⊆ α1 .
(3)
Hence, a seed alphabet is a chain in the inclusion ordering of seed letters. Let
us analyze what are the maximal seed alphabets wrt. inclusion. Clearly each
maximal seed alphabet B always contains the smallest and the largest seed letters
# and . Interestingly, each maximal B contains also @, as @ is comparable (by
inclusion) to any other seed letter.
subset seeds for protein similarity search
7
It can be shown that any maximal seed alphabet contains exactly 20 letters
that can be obtained by a stepwise merging of two subtrees rooted at immediate
descendants of some node v into the subtree rooted at v. Therefore, since a
binary tree with n leaves contains n − 1 internal nodes, a maximal seed alphabet
contains precisely 20 letters and can be specified by a permutation of internal
nodes in tree T .
Resulting alphabet Figure 3 shows alphabet Transitive-predefined designed through the approach of this Section. The alphabet has been designed
from the tree of Figure 2. Each line corresponds to a letter (amino acid partition). Among the alphabets obtained with different parameter values, alphabet
Transitive-predefined produced better seeds and will be used in the experimental part of this work (Section 5).
{CF Y W M LIV GP AT SN HQEDRK}
{CF Y W M LIV } {GP AT SN HQEDRK}
{CF Y W M LIV } {GP AT S} {N HQEDRK}
{CF Y W } {M LIV } {GP AT S} {N HQEDRK}
{CF Y W } {M LIV } {G} {P AT S} {N HQEDRK}
{C} {F Y W } {M LIV } {G} {P AT S} {N HQEDRK}
{C} {F Y W } {M LIV } {G} {P } {AT S} {N HQEDRK}
{C} {F Y } {W } {M LIV } {G} {P } {AT S} {N HQEDRK}
{C} {F } {Y } {W } {M LIV } {G} {P } {AT S} {N HQEDRK}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T S} {N HQEDRK}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N HQEDRK}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N HQED} {RK}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N HQED} {R} {K}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N H} {QED} {R} {K}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N } {H} {QED} {R} {K}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N } {H} {QE} {D} {R} {K}
{C} {F } {Y } {W } {M LIV } {G} {P } {A} {T } {S} {N } {H} {Q} {E} {D} {R} {K}
{C} {F } {Y } {W } {M L} {IV } {G} {P } {A} {T } {S} {N } {H} {Q} {E} {D} {R} {K}
{C} {F } {Y } {W } {M } {L} {IV } {G} {P } {A} {T } {S} {N } {H} {Q} {E} {D} {R} {K}
{C} {F } {Y } {W } {M } {L} {I} {V } {G} {P } {A} {T } {S} {N } {H} {Q} {E} {D} {R} {K}
Fig. 3. Alphabet Transitive-predefined designed using the tree of Figure 2. Each
line corresponds to a seed letter (amino acid partition)
4.2
Transitive alphabets using an ab initio clustering method
Hierarchical clustering of amino acids A prerequisite to the approach of
Section 4.1 is a given tree describing a hierarchical clustering of amino acid based
on some similarity measure. In this section, we describe an ab initio approach
that constructs a hierarchical clustering of amino acids from scratch, using a
likelihood measure.
As in Section 4, our goal here is to construct a family of seed letters verifying
(3). This family will be obtained with a simple greedy neighbor-joining clustering
algorithm, starting with the family of twenty amino acid singletons.
We start with the partition of amino acids into 20 singletons. This partition
corresponds to the # letter. For a current partition P = {C1 , . . . , Cn }, iteratively
apply the following procedure.
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M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
1 For each pair of sets Ck , C` ,
1.1 consider the set Bridge(Ck ,P
C` ) = {(ai , aj )|ai ∈ Ck , aj ∈ C` }.
1.2 compute F oreP rob(k, `) = P{fij |ai ∈ Ck , aj ∈ C` }
and
BackP rob(k, `) = {bi bj |ai ∈ Ck , aj ∈ C` },
1.3 compute L(k, `) = F oreP rob(k, `)/BackP rob(k, `)
2 Find the pair of sets (Ck , C` ) yielding the maximal L(k, `),
3 Merge Ck and C` into a new set, obtaining a new partition.
The rationale behind this simple procedure is that those two sets of amino
acid are merged together which produce the maximal increment in the likelihood
f (α)/b(α). An alternative method, when the likelihood of the whole resulting
set is maximized, yields biased results, as sets with a high likelihood tend to
“absorb” other sets.
Resulting alphabet An alphabet, called Transitive-ab-initio, obtained
with this greedy neighbor-joining approach is given in Figure 4. It will be used
in experiments presented later in Section 5.
{CF Y W HM LIV P GQERKN DAT S}
{CF Y W HM LIV } {P GQERKN DAT S}
{C} {F Y W HM LIV } {P GQERKN DAT S}
{C} {F Y W HM LIV } {P } {GQERKN DAT S}
{C} {F Y W H} {M LIV } {P } {GQERKN DAT S}
{C} {F Y W H} {M LIV } {P } {GAT S} {QERKN D}
{C} {F Y W H} {M LIV } {P } {G} {AT S} {QERKN D}
{C} {F Y W H} {M LIV } {P } {G} {AT S} {QERK} {N D}
{C} {F Y W } {H} {M LIV } {P } {G} {AT S} {QERK} {N D}
{C} {F Y W } {H} {M LIV } {P } {G} {A} {T S} {QERK} {N D}
{C} {F Y W } {H} {M LIV } {P } {G} {A} {T S} {QE} {RK} {N D}
{C} {F Y W } {H} {M L} {IV } {P } {G} {A} {T S} {QE} {RK} {N D}
{C} {F Y W } {H} {M L} {IV } {P } {G} {A} {T S} {QE} {RK} {N } {D}
{C} {F Y W } {H} {M L} {IV } {P } {G} {A} {T } {S} {QE} {RK} {N } {D}
{C} {F Y } {W } {H} {M L} {IV } {P } {G} {A} {T } {S} {QE} {RK} {N } {D}
{C} {F Y } {W } {H} {M L} {IV } {P } {G} {A} {T } {S} {Q} {E} {RK} {N } {D}
{C} {F Y } {W } {H} {M } {L} {IV } {P } {G} {A} {T } {S} {Q} {E} {RK} {N } {D}
{C} {F Y } {W } {H} {M } {L} {I} {V } {P } {G} {A} {T } {S} {Q} {E} {RK} {N } {D}
{C} {F } {Y } {W } {H} {M } {L} {I} {V } {P } {G} {A} {T } {S} {Q} {E} {RK} {N } {D}
{C} {F } {Y } {W } {H} {M } {L} {I} {V } {P } {G} {A} {T } {S} {Q} {E} {R} {K} {N } {D}
Fig. 4. Alphabet Transitive-ab-initio obtained with the method of Section 4.2
4.3
Non-hierarchical alphabets
Previous approaches (Sections 4.1 and 4.2) were based on requirement (3) specifying that letters of the seed alphabet should be embedded one into another
to form a “nested” hierarchy. This requirement is biologically motivated and,
on the other hand, computationally useful as it reduces considerably the space
of possible letters. However, this requirement is not necessary to implement the
direct indexing (see Introduction). Therefore, we also designed non-hierarchical
alphabets in order to compare them to hierarchical ones. We used the following
heuristic consisting in generating first a large number of seed candidates, and
selecting the ones with (1) high likelihood ratio, (2) a range of different weights.
subset seeds for protein similarity search
9
Resulting alphabet An alphabet obtained with the above heuristic, called
Non-tree-transitive, is shown in Figure 5. This alphabet will be used in the
experiments reported in Section 5.
{ARN DCQEGHILM KF P ST W Y V }
{ARN DQEGHILM KF P ST W Y V } {C}
{ARN DCQEHILM KF P ST W Y V } {G}
{ARN DQEHILM KF ST Y V } {CGP W }
{ARCQEHILM KF ST Y V } {N DGP W }
{ARN DCQEGHKP ST } {ILM F W Y V }
{ARN DQEGHKST } {CILM F W Y V } {P }
{ARN DQEHKP ST } {CW } {G} {ILM F Y V }
{ARN DQEKST } {CP } {GHW } {ILM F Y V }
{AGP ST } {RN DQEHK} {C} {ILM F W Y V }
{AP ST } {RN DQEHK} {CW } {G} {ILM F Y V }
{AGST } {RN DQEK} {C} {HF W Y } {ILM V } {P }
{AST } {RN DQEK} {CH} {G} {ILM V } {F W Y } {P }
{AST } {RQEHK} {N D} {CP } {G} {ILM V } {F W Y }
{AST } {RQK} {N H} {DE} {C} {G} {ILM V } {F W Y } {P }
{A} {RQK} {N } {DE} {C} {G} {H} {ILM V } {F Y } {P } {ST } {W }
{A} {RK} {N } {DE} {C} {QH} {G} {ILV } {M } {F Y } {P } {ST } {W }
{A} {RQK} {N D} {C} {E} {G} {H} {IV } {LM } {F W Y } {P } {ST }
{A} {RK} {N D} {C} {Q} {E} {G} {H} {IV } {LM } {F W Y } {P } {S} {T }
{A} {RK} {N } {D} {C} {Q} {E} {G} {H} {IV } {L} {M } {F Y } {P } {S} {T } {W }
{A} {R} {N } {D} {C} {QE} {G} {H} {I} {L} {K} {M } {F W Y } {P } {S} {T } {V }
{A} {R} {N } {D} {C} {Q} {E} {G} {H} {I} {L} {K} {M } {F } {P } {S} {T } {W } {V }
Fig. 5. Non-hierarchical alphabet Non-tree-transitive.
5
Experiments
This section describes the experiments we made to test the efficiency of seeds we
designed with different methods of previous sections. Sections 5.1-5.3 describe
the experimental protocol, from the assignment of background and foreground
probabilities, to the seed design. In Section 5.4, we analyze the power of different
seed models proposed in Sections 3-4 with respect to probabilistic models.
5.1
Probability assignment and alphabet generation
First of all, we derived probabilistic models in accordance with the BLOSUM62
data from the original paper [22]. We obtained the BLOCKS database (version
5) [23] and the software of [22] to infer Bernoulli probabilities for the background and foreground alignment models. These probabilities have been used
throughout the whole pipeline of experiments.
Different seed alphabets have then been generated by the methods presented
in Section 3 (alphabet Non-transitive), Section 4.1 (alphabet
Transitive-predefined), Section 4.2 (alphabet Transitive-ab-initio) and
Section 4.3 (alphabet Non-tree-transitive).
5.2
Seed design
To each alphabet, we applied a seed design procedure that we briefly describe
now. Since each seed (or seed family) is characterized by two parameters – sensitivity and selectivity – it can be associated with a point on a 2-dimensional plot.
10
M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
Best seeds are then defined to be those which belong to the Pareto set among
all seeds, i.e. those than cannot be strictly improved by increasing sensitivity,
selectivity, or both.
For different selectivity levels, we designed good seed families containing one
to six individual seeds, among which the best family was selected. In each seed
family, each individual seed has been assumed to have approximately the same
weight, within 5% tolerance. This requirement is natural as in the case of divergent weights, seeds with lower weight would dominantly affect the performance.
In practice, having individual seeds of similar weight allows an efficient parallel
implementation (see e.g. [17]).
Estimation of sensitivity of individual seeds or seed families has been done
with the algorithm described in [1] and implemented in the Iedera software,
available at http://bioinfo.lifl.fr/yass/iedera.php. The selectivity of an individual seed has been computed according to the definition (Section 2). For a
seed family, its selectivity has been lower-estimated by summing the background
probabilities of individual seeds.
Seed family design has been done using a hill climbing heuristics (see [24,25,11])
alternating seed generation and seed estimation steps. All experiments were conducted for alignment lengths 16 and 32.
5.3
Blastp and the vector seed family from [4]
Our goal is to compare between different seed design approaches proposed in
this paper, but also to benchmark them against other reference seeding methods.
We used two references: the Blastp seeding method and the family of vector
seeds proposed in [4]. Both of them use a score (or weight) resulting from the
accumulative contribution of several neighboring positions to define a hit (see
Introduction). Therefore, they use a more powerful (and also more costly to
implement) formalism of seeding.
To estimate the sensitivity and selectivity of those seeds, we modified our
methods described in the previous section by representing an alignment by a
sequence of possible individual scores. Foreground and background probability
of each score is easily computed from those for amino acid pairs. After that,
sensitivity and selectivity is computed similarly to the previous case.
5.4
Results
We compare the performance of the different approaches by plotting ROC curves
of Pareto-optimal sets of seeds on the selectivity/sensitivity graph. The two plots
in Figure 6 show the results for alignment length 16 and 32 respectively. The two
first polylines show the performance of Blastp with word size 3 and the vector
seed family from [4], for different score thresholds. The other curves show the
performances of different seed alphabets from Sections 3-4 represented by the
Pareto-optimal seeds (seed families) that we were able to construct over those
alphabets. As mentioned earlier in Section 5.2, each time we selected the best
seed family among those with different number of individual seeds. Typically
subset seeds for protein similarity search
11
Fig. 6. ROC curves of seed performance measured on the probabilistic model
B62 L16
0.9
13
10
14
sensitivity
0.8
15
11
0.7
12
Blastp (thr.)
Protein vector seeds (thr.)
Transitive-predefined
Transitive-ab-initio
Non-tree-transitive
Non-transitive
0.6
0.996
0.997
0.998
0.999
selectivity
B62 L32
0.99
13
0.98
14
10
0.97
sensitivity
0.96
0.95
15
11
0.94
0.93
0.92
0.91
0.9
16
Blastp (thr.)
Protein vector seeds (thr.)
Transitive-predefined
Transitive-ab-initio
Non-tree-transitive
Non-transitive
0.996
12
0.997
0.998
selectivity
0.999
12
M. Roytberg, A. Gambin, L. Noé, S. Lasota, E. Szczurek, G. Kucherov
(but not exclusively), points on the plots correspond to seed families with 3 to
5 seeds. Typically, the seed span ranges between 3 and 5 (respectively, 3 and 6)
for alignment length 16 (respectively, 32). Seeds with langer span (> 4) tend to
occur in seed families with larger number of seeds (> 3).
We observe that non-transitive seeds over the alphabet of Section 3 are comparable in performance with the vector seed family from [4] and clearly outperforms seeds over other alphabets. This result is interesting in itself, although
this alphabet is unpractical in many cases, due to its incompatibility with the
transitivity condition.
As for the other alphabets, they roughly show a comparable performance
among them. Note that using non-hierarchical alphabet (Section 4.3) does not
bring much of improvement, which justifies condition (3). For the alignment
length 16, our seeds perform comparably to Blastp, with a slightly better performance for high thresholds and a slightly worse performance for low thresholds.
On the other hand, for alignments of length 32, our seeds clearly outperform
Blastp.
6
Conclusion
The main conclusion of our work is that although the subset seed model is less
expressive than the method of accumulative score used in Blastp, carefully
designed subset seeds can reach the same or even a higher performance. To put
it informally, the use of the accumulative score in defining a hit can, without
loss of performance, be replaced by a careful distinction between different amino
acid matches without using any scoring system. From a practical point of view,
subset seeds can provide a more efficient implementation, especially for largescale protein comparisons, due to a much smaller number of accesses to the
hash table. In particular, this can be very useful for parallel implementations or
specialized hardware (see e.g. [17]).
Note that the seed design heuristic sketched in Section 5.2 does not guarantee
to compute optimal seeds, and therefore our seeds could potentially be further
improved by a more advanced design procedure, possibly bringing a further
increase in performance. This is especially true for seeds of large weight (due to
a bigger number of those), for which our seed design procedure could produce
non-optimal seeds, thus explaining some “drop-offs” in high-selectivity parts of
plots of Figure 6.
As far as further research is concerned, the question of efficient seed design
remains an open issue. Improvements of the hill climbing heuristics used in this
work are likely to be possible.
Acknowledgements Parts of this work have been done during visits to LIFL of
Ewa Szczurek (June-August 2006), Anna Gambin and Slawomir Lasota (August 2006) and Mikhail Roytberg (October-December 2006). Those visits were
supported by the ECO-NET and Polonium programs of the French Ministry of
Foreign Affairs.
subset seeds for protein similarity search
13
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